Контрольные задания
Вопрос:Фото задания: Задание 3. Вычисли: \(\sqrt{49/16}-\sqrt{25/36}\); \(\sqrt{4/81}+\sqrt{25/36}\); \(\sqrt{4/81}-\sqrt{1/36}\);…Фото задания

Ответ:

  1. \(\sqrt{\frac{49}{16}}-\sqrt{\frac{25}{36}}=\frac74-\frac56=\frac{21-10}{12}=\frac{11}{12}\).
  2. \(\sqrt{\frac4{81}}+\sqrt{\frac{25}{36}}=\frac29+\frac56=\frac4{18}+\frac{15}{18}=\frac{19}{18}\).
  3. \(\sqrt{\frac4{81}}-\sqrt{\frac1{36}}=\frac29-\frac16=\frac4{18}-\frac3{18}=\frac1{18}\).
  4. \(\sqrt{\frac49}+\sqrt{\frac1{36}}=\frac23+\frac16=\frac56\).
  5. \(15\sqrt{\frac{324+225}{625}}+16=15\cdot\frac{\sqrt{549}}{25}+16=16+\frac{9\sqrt{61}}5\).
  6. \(-2\sqrt{\frac{49}{64}}+17=-2\cdot\frac78+17=17-\frac74=\frac{61}{4}\).
  7. \(0,5\sqrt{\frac4{25}}+\sqrt{\frac{25}{4}}=0,5\cdot\frac25+\frac52=\frac15+\frac52=\frac{27}{10}\).
  8. \(1000\sqrt{\frac{0,0001}{100}}+5=1000\cdot0,001+5=6\).
  9. \(\sqrt{54\cdot48\cdot128}=\sqrt{2^{12}\cdot3^4}=2^6\cdot3^2=576\).

Ответ: \(\frac{11}{12};\frac{19}{18};\frac1{18};\frac56;16+\frac{9\sqrt{61}}5;\frac{61}{4};\frac{27}{10};6;576\).